There is definitely some benefit to be gained by using a crop sensor camera when longer focal length is desireable. It is one of the reasons compact "superzoom" cameras can give fields of view equivalent to 1000mm+ focal lengths on a full frame camera with a much smaller lens than would be required to get that same FoV using a full frame sensor camera.

If the pixel density is the same on a FF camera and an APS-C camera, then there would be little to no benefit. But the pixel density is rarely the same. A typical APS-C camera might have a 20MP sensor that gives a pixel spacing of about 4 microns. A 22MP FF camera has a pixel spacing of 6.25 microns.

The crop factor of a particular sensor is based on *linear* measurements, but pixel density is measured in terms of pixels per area. This means the number of pixels on a FF sensor that fall within the space covered by a 1.5X APS-C sensor is not 1/1.5X, but 1/2.25X of the total number of pixels on the sensor. In the case of our typical 22MP FF camera, if we crop the image by 1.5X in the linear measurements we are only left with a pixel count of just under 10MP. In the case of a 1.6X APS-C sensor it would only be about 8.6MP.

If you magnify the image projected by the lens, such as is the case with a teleconverter, you spread the light thinner and give up aperture in terms of the f-number. But if you increase magnification when printing or displaying the image you don't lose any aperture in terms of exposure